CN104052697A - Interference alignment method based on two-layer precoding structure in MIMO-IBC system - Google Patents

Abstract

The invention belongs to the technical field of communication, and discloses an interference alignment method based on a two-layer pre-coding structure and suitable for a multiple input multiple output-interference broadcast channel (MIMO-IBC) system. In the MIMO-IBC system, interference among communities and interference among users are main factors for limiting channel capacity. The method includes the steps of firstly, aligning ICI signals through base station outer layer pre-coding, eliminating the ICI signals through a receiving matrix, and finally eliminating IUI signals through base station inner layer pre-coding. According to the method, when the number of antennas of a base station meets the condition, the ICI signals can be aligned in a low-dimensional interference signal sub-space through closed solution, and otherwise, the ICI signals are aligned in or gets close to the low-dimensional interference signal sub-space through loop iteration. By means of the method, the ICI signals and the IUI signals can be effectively eliminated, the system capacity can be remarkably improved; the zero-forcing technology can be adopted at a receiving end, and therefore receiving is simplified, and meanwhile the requirement for the number of antennas at the receiving end is low.

Description

Translated fromChinese

MIMO-IBC系统中基于两层预编码结构的干扰对齐方法Interference alignment method based on two-layer precoding structure in MIMO-IBC system

技术领域technical field

本发明涉及通信技术领域，具体涉及多输入多输出干扰广播信道(Interference Broadcast Channel，IBC)系统中一种基于两层预编码结构的干扰对齐(Interference Alignment，IA)方法。The present invention relates to the field of communication technology, in particular to an Interference Alignment (IA) method based on a two-layer precoding structure in a MIMO Interference Broadcast Channel (IBC) system.

背景技术Background technique

在MIMO系统中，ICI是获取高频谱利用率的主要制约因素。小区间干扰(Inter-Cell Interference，ICI)和用户间干扰(Inter-UserInterference，IUI)是制约信道容量的主要因素。近年来，干扰对齐(Interference Alignment，IA)技术的提出为MIMO干扰信道(Interference Channel，IC)中ICI信号的管理提出了一种新的思路：接收端将ICI信号对齐在特定的干扰子空间内，而干扰子空间的正交子空间则用于期望信号的传输。研究表明，在MIMO-IC中，运用IA技术，每个小区能获得1/2的自由度(Degrees of Freedom，DoF)。In MIMO systems, ICI is the main constraint factor for obtaining high spectrum utilization. Inter-cell interference (Inter-Cell Interference, ICI) and inter-user interference (Inter-User Interference, IUI) are the main factors restricting channel capacity. In recent years, the introduction of Interference Alignment (IA) technology has proposed a new idea for the management of ICI signals in MIMO Interference Channel (Interference Channel, IC): the receiver aligns the ICI signals in a specific interference subspace , while the orthogonal subspace of the interference subspace is used for the transmission of the desired signal. Studies have shown that in MIMO-IC, each cell can obtain 1/2 degree of freedom (Degrees of Freedom, DoF) by using IA technology.

在早期研究中，IA技术多用于干扰信道，其主要研究集中在IA技术所能获得的最优DoF、系统容量的上下限、实现IA所需要的收发天线数等问题。而在多小区MIMO-IBC系统中，一个基站对应多个用户，因此，用户不仅接收到ICI信号，还接收到IUI信号，这比单纯的MIMO-IC要复杂很多，而目前对多小区MIMO-IBC系统中IA技术的研究并不是很多。In early research, IA technology was mostly used for interfering channels, and the main researches focused on the optimal DoF obtained by IA technology, the upper and lower limits of system capacity, and the number of transmitting and receiving antennas required to realize IA. In the multi-cell MIMO-IBC system, one base station corresponds to multiple users. Therefore, users not only receive ICI signals, but also receive IUI signals. This is much more complicated than pure MIMO-IC. Currently, multi-cell MIMO- There are not many researches on IA technology in IBC system.

在多小区多用户场景中，IA技术能有效地消除ICI信号和IUI信号，从而显著地提升信道容量。目前，针对多小区多用户环境下的IA算法研究可大致分为两类：迭代算法和直接算法。迭代算法通过不断地循环迭代预编码矩阵和接收矩阵来实现IA，而直接算法则用闭式求解方式。迭代算法往往能获得较高的信道容量，尤其在低信噪比条件下；但是，迭代算法复杂度高、收敛速度慢。而直接算法主要针对2个小区的MIMO-IBC系统，通过联合设计预编码矩阵和接收矩阵来实现干扰对齐，且要求收、发天线数目必须满足特定条件。In multi-cell multi-user scenarios, IA technology can effectively eliminate ICI signals and IUI signals, thereby significantly improving channel capacity. At present, research on IA algorithms in a multi-cell multi-user environment can be roughly divided into two categories: iterative algorithms and direct algorithms. The iterative algorithm implements IA by continuously iterating the precoding matrix and the receiving matrix, while the direct algorithm uses a closed solution method. The iterative algorithm can often obtain higher channel capacity, especially under the condition of low signal-to-noise ratio; however, the iterative algorithm has high complexity and slow convergence speed. The direct algorithm is mainly aimed at the MIMO-IBC system of two cells, and achieves interference alignment by jointly designing the precoding matrix and receiving matrix, and requires that the number of receiving and transmitting antennas must meet certain conditions.

发明内容Contents of the invention

有鉴于此，本发明所要解决的技术问题是，针对多小区MIMO-IBC系统，采用迭代算法复杂度高、收敛速度慢；采用直接算法通过联合设计预编码矩阵和接收矩阵实现干扰对齐，要求收、发天线数目必须满足特定条件。根据多小区MIMO-IBC系统的特点，提出一种基于两层预编码结构的干扰对齐方法。In view of this, the technical problem to be solved by the present invention is that for a multi-cell MIMO-IBC system, the iterative algorithm has high complexity and slow convergence speed; the direct algorithm is used to jointly design the precoding matrix and the receiving matrix to achieve interference alignment, requiring the receiving , The number of transmitting antennas must meet certain conditions. According to the characteristics of multi-cell MIMO-IBC system, an interference alignment method based on two-layer precoding structure is proposed.

本发明解决上述技术问题的技术方案是，设计一种基于两层预编码结构的干扰对齐方法。系统场景设置为：小区数为G，小区内用户数为K，每个用户均对应d个数据流，所有小区基站天线数均为N_t、用户天线数均为N_r，并用(G,N_t)×(K,N_r)来标识，小区g中用户k用符号g_k来表示，基站只向本小区内的用户传输信号。构造任意Kd阶非奇异矩阵{Q_gl}(g≠l；g,l＝1,...G)，设计基站的外层预编码矩阵将所有ICI信号对齐在一个低维度的干扰子空间内；接收端设计接收矩阵以消除ICI信号；设计基站内层预编码矩阵以消除IUI信号。其中，表示维度为N_t×Kd的复矩阵，表示维度为d×N_r的复矩阵，表示维度为Kd×d的复矩阵。()^H表示求取矩阵的共轭转置。具体包括如下步骤：The technical solution of the present invention to solve the above technical problem is to design an interference alignment method based on a two-layer precoding structure. The system scenario is set as follows: the number of cells is G, the number of users in the cell is K, each user corresponds to d data streams, the number of base station antennas in all cells is N_t , the number of user antennas is N_r , and (G,N_t )×(K, N_r ), the user k in the cell g is represented by the symbol g_k , and the base station only transmits signals to the users in this cell. Construct any Kd-order non-singular matrix {Q_gl }(g≠l; g,l=1,...G), and design the outer precoding matrix of the base station Align all ICI signals in a low-dimensional interference subspace; design the receiving matrix at the receiving end To eliminate the ICI signal; design the inner layer precoding matrix of the base station to eliminate the IUI signal. in, Represents a complex matrix of dimension N_t ×Kd, Represents a complex matrix of dimension d×N_r , Represents a complex matrix of dimension Kd×d. ()^H means to find the conjugate transpose of the matrix. Specifically include the following steps:

设计基站的外层预编码矩阵将所有ICI信号对齐在一个低维度的干扰子空间内；设计用于消除ICI信号的接收矩阵因此，是ICI信号的零空间。Design the outer precoding matrix of the base station Align all ICI signals within a low-dimensional interference subspace; design a receive matrix to cancel ICI signals therefore, is the null space of the ICI signal.

设计基站的内层预编码矩阵用于消除IUI信号，因此，B_gk是IUI信号的零空间，即：$B_{g_k}\⋐\mathrm{null}\left({[{\left(U_{g_1}^H{H}_{g_1,g}{P}_g\right)}^H,...,{\left(U_{g_{k-1}}^H{H}_{g_{k-1},g}{P}_g\right)}^H,{\left(U_{g_{k+1}}^H{H}_{g_{k+1},g}{P}_g\right)}^H,...,{\left(U_{g_k}^H{H}_{g_k,g}{P}_g\right)}^H]}^H\right)$,其中表示接收矩阵，表示基站到本小区用户的平坦瑞利衰落信道,null()表示求取矩阵的零空间。Design the inner precoding matrix of the base station is used to eliminate the IUI signal, therefore, B_gk is the null space of the IUI signal, namely:$B_{g_k}\⋐\mathrm{null}\left({[{\left(u_{g_1}^h{h}_{g_1,g}{P}_g\right)}^h,...,{\left(u_{g_{k-1}}^h{h}_{g_{k-1},g}{P}_g\right)}^h,{\left(u_{g_{k+1}}^h{h}_{g_{k+1},g}{P}_g\right)}^h,...,{\left(u_{g_k}^h{h}_{g_k,g}{P}_g\right)}^h]}^h\right)$ ,in represents the receiving matrix, Indicates the flat Rayleigh fading channel from the base station to the user in the cell, and null() indicates the null space of the matrix.

基站外层预编码矩阵需满足将来自不同基站的干扰信号对齐或逼近到一低维子空间，比如，对于小区g中的用户，将ICI信号对齐或逼近到来自第g+1小区的干扰信号子空间。在整个系统中，基站外层预编码矩阵满足下式：Base station outer layer precoding matrix It is necessary to align or approximate interference signals from different base stations to a low-dimensional subspace, for example, for users in cell g, align or approximate ICI signals to the interference signal subspace from cell g+1. In the whole system, the base station outer precoding matrix Satisfies the following formula:

$\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>H</span>h</span>}}\mathrm{<span><span>p</span>p</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}$

$\mathrm{<span><span>p</span>p</span>}<span><span>=</span>=</span>\left[\begin{array}{c}\mathrm{<span><span>vec</span>vec</span>}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>)</span>)</span>\\ \mathrm{<span><span>vec</span>vec</span>}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ \mathrm{<span><span>vec</span>vec</span>}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>G</span>G</span>}}<span><span>)</span>)</span>\end{array}\right]$

其中，I是与{Q_gl}(g≠l；g,l＝1,...G)同阶的单位阵，表示基站l到小区g的平坦瑞利衰落信道，表示基站g的外层预编码矩阵，O表示KdKN_r×KdN_t维的零矩阵，矩阵()^T表示求取矩阵的转置，vec()表示求取矩阵的列向量化函数。Wherein, I is an identity matrix with the same order as {Q_gl }(g≠l; g,l=1,...G), Denotes the flat Rayleigh fading channel from base station l to cell g, Represents the outer precoding matrix of base station g, O represents the zero matrix of KdKN_r ×KdN_t dimension, the matrix ()^T means to obtain the transpose of the matrix, and vec() means to obtain the column vectorization function of the matrix.

接收矩阵在接收端将信号空间分为干扰信号子空间和期望信号子空间，用户间干扰信号和小区间干扰信号将被对齐到干扰信号子空间，期望信号则被对齐到期望信号子空间，期望信号子空间的维度大于等于要传输的数据流个数d。当N_t＞(G-2)KN_r时，{Q_gl}(g≠l；g,l＝1,...G)为任意Kd阶非奇异矩阵，或任意非零常数，p都有非零解；当N_t≤(G-2)KN_r时，通过循环迭代矩阵{Q_gl}(g≠l；g,l＝1,...G)与向量p，使得或接近0。此外，当N_t＝(G-2)KN_r时，根据块矩阵的性质，通过矩阵运算可知{Q_gl}(g≠l；g,l＝1,...G)为某一系列非零常数时，使得成立，p有非零解。其中，rank()表示求取矩阵的秩，||||表示求取向量的2-范数。The receiving matrix divides the signal space into the interference signal subspace and the desired signal subspace at the receiving end. The inter-user interference signal and the inter-cell interference signal will be aligned to the interference signal subspace, and the desired signal will be aligned to the desired signal subspace. The dimension of the signal subspace is greater than or equal to the number d of data streams to be transmitted. When N_t >(G-2)KN_r , {Q_gl }(g≠l; g,l=1,...G) is any Kd order non-singular matrix, or any non-zero constant, p has Non-zero solution; when N_t ≤ (G-2)KN_r , the matrix {Q_gl }(g≠l; g,l=1,...G) and the vector p are iterated through the loop, so that or close to 0. In addition, when N_t =(G-2)KN_r , according to the properties of the block matrix, it can be seen that {Q_gl }(g≠l; g,l=1,...G) is a series of non At zero constant, such that established, p has a non-zero solution. Among them, rank() means to find the rank of the matrix, and |||| means to find the 2-norm of the vector.

当将来自第g+1小区的干扰信号对齐在来自于剩余小区干扰信号组成的子空间内时，基站外层预编码矩阵则需满足公式：When the interference signal from the g+1th cell is aligned in the subspace composed of interference signals from the remaining cells, the outer precoding matrix of the base station The formula needs to be satisfied:

至此，对于小区g中的用户k而言，IUI信号被对齐在的正交子空间内，ICI信号也被对齐或逼近到的正交子空间内，因此，使用该方法可使多小区MIMO-IBC系统中的干扰信号得以消除。其中，span()表示矩阵的列向量张成的子空间。从该发明设计过程中可知，接收矩阵为矩阵列向量的正交矩阵，所以，本发明可有效地减少接收端天线数和处理复杂度，从而降低了移动设备设计成本。So far, for user k in cell g, the IUI signal is aligned at In the orthogonal subspace of , the ICI signal is also aligned or approximated to Therefore, using this method, the interference signal in the multi-cell MIMO-IBC system can be eliminated. Among them, span() represents the subspace spanned by the column vectors of the matrix. It can be seen from the design process of the invention that the receiving matrix for the matrix An orthogonal matrix of column vectors, so the present invention can effectively reduce the number of receiving end antennas and processing complexity, thereby reducing the design cost of mobile equipment.

附图说明Description of drawings

图1MIMO-IBC系统示意图；Fig. 1 Schematic diagram of MIMO-IBC system;

图2本发明实现干扰对齐的方法示意图；Fig. 2 is a schematic diagram of a method for realizing interference alignment in the present invention;

图3本发明实现流程图；Fig. 3 realizes flow chart of the present invention;

图4本发明干扰对齐效果示意图；Fig. 4 is a schematic diagram of interference alignment effect of the present invention;

图5系统容量比较图。Figure 5 system capacity comparison chart.

具体实施方式Detailed ways

一般多小区MIMO-IBC系统场景为：小区数为G，每一小区只包含一个基站、基站同时为多个用户服务，在g小区中共有K_g个用户，基站和用户k分别配有M_g和根天线，基站向用户k发送个数据流，用标记一般场景下的MIMO-IBC系统。The general multi-cell MIMO-IBC system scenario is as follows: the number of cells is G, each cell contains only one base station, and the base station serves multiple users at the same time, there are K_g users in g cells, and the base station and user k are respectively equipped with M_g and root antenna, the base station sends to user k data stream, with Label MIMO-IBC systems in general scenarios.

本发明中多小区MIMO-IBC系统场景设置为：小区数为G，小区内用户数为K，每个用户均对应d个自由度，所有小区基站天线数均为N_t、用户天线数均为N_r，并用(G,N_t)×(K,N_r)来标识，小区g中用户k用符号g_k来表示，基站只向本小区内的用户传输信号。In the present invention, the multi-cell MIMO-IBC system scenario is set as follows: the number of cells is G, the number of users in the cell is K, each user corresponds to d degrees of freedom, the number of base station antennas in all cells is N_t , and the number of user antennas is N_r , and marked by (G,N_t )×(K,N_r ), user k in cell g is represented by symbol g_k , and the base station only transmits signals to users in this cell.

图1所示为G个小区的MIMO-IBC系统，在每个小区中，一个基站服务于多个用户。在g小区中共有K_g个用户，基站和用户k分别配有M_g和根天线，基站向用户k发送个数据流，小区g中用户k用符号g_k来表示。基站之间共享信道状态信息(Channel State Information，CSI)，而不共享数据信息。用表示一个一般场景下的MIMO-IBC系统。用户在接收到期望信号的同时，也接收到本小区用户间的干扰信号和相邻小区的干扰信号，此时，用户g_k接收到的信号可表示为：FIG. 1 shows a MIMO-IBC system with G cells. In each cell, one base station serves multiple users. There are K_g users in cell g, the base station and user k are equipped with M_g and root antenna, the base station sends to user k data stream, User k in cell g is represented by the symbol g_k . The base stations share channel state information (Channel State Information, CSI) instead of sharing data information. use Represents a MIMO-IBC system in a general scenario. When the user receives the expected signal, he also receives the interference signal between the users of the cell and the interference signal of the adjacent cell. At this time, the signal received by the user g_k can be expressed as:

${\mathrm{<span><span>y</span>the\; y</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}<span><span>=</span>=</span>{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>g</span>g</span>}}{\mathrm{<span><span>V</span>V</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}{\mathrm{<span><span>s</span>the\; s</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}<span><span>+</span>+</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}<span><span>\&NotEqual;</span>\&NotEqual;</span>\mathrm{<span><span>k</span>k</span>}}{\overset{{\mathrm{<span><span>K</span>K</span>}}_{\mathrm{<span><span>g</span>g</span>}}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>g</span>g</span>}}{\mathrm{<span><span>V</span>V</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>i</span>i</span>}}}{\mathrm{<span><span>s</span>the\; s</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>i</span>i</span>}}}<span><span>+</span>+</span>\underset{\mathrm{<span><span>l</span>l</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>l</span>l</span>}<span><span>\&NotEqual;</span>\&NotEqual;</span>\mathrm{<span><span>g</span>g</span>}}{\overset{\mathrm{<span><span>G</span>G</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{{\mathrm{<span><span>K</span>K</span>}}_{\mathrm{<span><span>l</span>l</span>}}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>l</span>l</span>}}{\mathrm{<span><span>V</span>V</span>}}_{{\mathrm{<span><span>l</span>l</span>}}_{\mathrm{<span><span>i</span>i</span>}}}{\mathrm{<span><span>s</span>the\; s</span>}}_{{\mathrm{<span><span>l</span>l</span>}}_{\mathrm{<span><span>i</span>i</span>}}}<span><span>+</span>+</span>{\mathrm{<span><span>n</span>no</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}<span><span>,</span>,</span>$

其中，表示基站l到用户g_k的平坦瑞利衰落信道；表示基站g传输给用户g_k的信号；表示用于信号的预编码矩阵，满足功率限制条件：表示用户g_k接收到的噪声，为独立同分布的复高斯向量，满足每个用户通过接收矩阵解码期望信号，假设用户g_k通过接收矩阵处理后的信号表示为：相应用户g_k的数据速率则可表示为：in, Indicates the flat Rayleigh fading channel from base station l to user g_k ; Indicates the signal transmitted by base station g to user g_k ; Indicates that it is used to signal The precoding matrix satisfies the power constraint condition: Indicates the noise received by user g_k , which is an independent and identically distributed complex Gaussian vector, satisfying Each user decodes the desired signal through the receiving matrix, assuming that the user g_k passes the receiving matrix The processed signal is expressed as: The data rate of the corresponding user g_k can then be expressed as:

${\mathrm{<span><span>R</span>R</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}<span><span>=</span>=</span>{\mathrm{<span><span>log</span>log</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>\{</span>\{</span>\mathrm{<span><span>det</span>det</span>}<span><span>[</span>[</span>\mathrm{<span><span>I</span>I</span>}<span><span>+</span>+</span>\frac{{\mathrm{<span><span>U</span>u</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}^{\mathrm{<span><span>H</span>h</span>}}{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>g</span>g</span>}}{\mathrm{<span><span>V</span>V</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}{\mathrm{<span><span>V</span>V</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}^{\mathrm{<span><span>H</span>h</span>}}{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>g</span>g</span>}}^{\mathrm{<span><span>H</span>h</span>}}{\mathrm{<span><span>U</span>u</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}}{\underset{<span><span>(</span>(</span>\mathrm{<span><span>g</span>g</span>}<span><span>,</span>,</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span><span><span>\&NotEqual;</span>\&NotEqual;</span><span><span>(</span>(</span>\mathrm{<span><span>l</span>l</span>}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}{\mathrm{<span><span>U</span>u</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}^{\mathrm{<span><span>H</span>h</span>}}{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>l</span>l</span>}}{\mathrm{<span><span>V</span>V</span>}}_{{\mathrm{<span><span>l</span>l</span>}}_{\mathrm{<span><span>i</span>i</span>}}}{\mathrm{<span><span>V</span>V</span>}}_{{\mathrm{<span><span>l</span>l</span>}}_{\mathrm{<span><span>i</span>i</span>}}}^{\mathrm{<span><span>H</span>h</span>}}{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>l</span>l</span>}}^{\mathrm{<span><span>H</span>h</span>}}{\mathrm{<span><span>U</span>u</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}<span><span>+</span>+</span>{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}^{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>U</span>u</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}^{\mathrm{<span><span>H</span>h</span>}}{\mathrm{<span><span>U</span>u</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}}<span><span>]</span>]</span><span><span>\}</span>\}</span>$

其中，||||表示求取向量的2-范数，E{}表示求取期望操作，det{}表示求取矩阵的行列式值。Among them, |||| means to find the 2-norm of the vector, E{} means to find the expected operation, and det{} means to find the determinant value of the matrix.

为了有效地解码出期望信号，接收矩阵在接收端将信号空间分为干扰信号子空间和期望信号子空间，用户间干扰信号和小区间干扰信号将被对齐到干扰信号子空间，期望信号则被对齐到期望信号子空间，因此，期望信号子空间的维度不能小于要传输的数据流个数为此，线性IA的条件可表示为：In order to effectively decode the desired signal, the receiving matrix divides the signal space into the interference signal subspace and the desired signal subspace at the receiving end, the inter-user interference signal and the inter-cell interference signal will be aligned to the interference signal subspace, and the desired signal is Aligned to the desired signal subspace, therefore, the dimension of the desired signal subspace cannot be smaller than the number of data streams to be transmitted For this, the condition for linear IA can be expressed as:

$\left\{\begin{array}{c}{\mathrm{<span><span>U</span>u</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}^{\mathrm{<span><span>H</span>h</span>}}{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>l</span>l</span>}}{\mathrm{<span><span>V</span>V</span>}}_{{\mathrm{<span><span>l</span>l</span>}}_{\mathrm{<span><span>i</span>i</span>}}}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span><span><span>\&ForAll;</span>\&ForAll;</span>\mathrm{<span><span>l</span>l</span>}<span><span>\&NotEqual;</span>\&NotEqual;</span>\mathrm{<span><span>g</span>g</span>}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}<span><span>\&Element;</span>\&Element;</span><span><span>\{</span>\{</span>\mathrm{<span><span>1,2</span>1,2</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>{\mathrm{<span><span>K</span>K</span>}}_{\mathrm{<span><span>l</span>l</span>}}<span><span>\}</span>\}</span>\\ {\mathrm{<span><span>U</span>u</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}^{\mathrm{<span><span>H</span>h</span>}}{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>g</span>g</span>}}{\mathrm{<span><span>V</span>V</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>i</span>i</span>}}}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}<span><span>,</span>,</span><span><span>\&ForAll;</span>\&ForAll;</span>\mathrm{<span><span>i</span>i</span>}<span><span>\&NotEqual;</span>\&NotEqual;</span>\mathrm{<span><span>k</span>k</span>}\\ \mathrm{<span><span>rank</span>rank</span>}<span><span>(</span>(</span>{\mathrm{<span><span>U</span>u</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}^{\mathrm{<span><span>H</span>h</span>}}{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>g</span>g</span>}}{\mathrm{<span><span>V</span>V</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>d</span>d</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}<span><span>,</span>,</span><span><span>\&ForAll;</span>\&ForAll;</span>\mathrm{<span><span>g</span>g</span>}<span><span>,</span>,</span>\mathrm{<span><span>k</span>k</span>}\end{array}\right.$

其中，rank()表示求取矩阵的秩。Among them, rank() means to find the rank of the matrix.

图2所示为本发明提出的基于两层预编码结构的IA实现示意图，假设系统具有对称天线数，每个小区均有一个基站、K个用户，每个用户均对应d个数据流，所有基站天线数均为N_t＝M_g,(g＝1,...G)、用户天线数均为此系统用(G,N_t)×(K,N_r)来标记，小区g中用户k用符号g_k来表示，基站只向本小区内的用户传输信号。基站共设置两层预编码，内层预编码记作用于消除IUI信号；外层预编码则记作用于对齐ICI信号。用户g_k通过接收矩阵处理后的信号表示为：Figure 2 is a schematic diagram of the IA implementation based on the two-layer precoding structure proposed by the present invention. It is assumed that the system has a symmetrical number of antennas, and each cell has a base station and K users, and each user corresponds to d data streams. All The number of base station antennas is N_t = M_g , (g=1,...G), and the number of user antennas is This system is marked by (G,N_t )×(K,N_r ), user k in cell g is represented by symbol g_k , and the base station only transmits signals to users in this cell. There are two layers of precoding in the base station, and the inner layer of precoding is denoted as Used to eliminate the IUI signal; the outer precoding is recorded as Used to align ICI signals. User g_k receives matrix The processed signal is expressed as:

$\stackrel{<span><span>^</span>^</span>}{{\mathrm{<span><span>s</span>the\; s</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}}<span><span>=</span>=</span>{\mathrm{<span><span>U</span>u</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}^{\mathrm{<span><span>H</span>h</span>}}{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>g</span>g</span>}}{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>g</span>g</span>}}{\mathrm{<span><span>B</span>B</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}{\mathrm{<span><span>s</span>the\; s</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}<span><span>+</span>+</span>{\mathrm{<span><span>U</span>u</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}^{\mathrm{<span><span>H</span>h</span>}}\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}<span><span>\&NotEqual;</span>\&NotEqual;</span>\mathrm{<span><span>k</span>k</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>g</span>g</span>}}{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>g</span>g</span>}}{\mathrm{<span><span>B</span>B</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>i</span>i</span>}}}{\mathrm{<span><span>s</span>the\; s</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>i</span>i</span>}}}<span><span>+</span>+</span>{\mathrm{<span><span>U</span>u</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}^{\mathrm{<span><span>H</span>h</span>}}\underset{\mathrm{<span><span>l</span>l</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}<span><span>,</span>,</span>\mathrm{<span><span>l</span>l</span>}<span><span>\&NotEqual;</span>\&NotEqual;</span>\mathrm{<span><span>g</span>g</span>}}{\overset{\mathrm{<span><span>G</span>G</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>K</span>K</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>l</span>l</span>}}{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>l</span>l</span>}}{\mathrm{<span><span>B</span>B</span>}}_{{\mathrm{<span><span>l</span>l</span>}}_{\mathrm{<span><span>i</span>i</span>}}}{\mathrm{<span><span>s</span>the\; s</span>}}_{{\mathrm{<span><span>l</span>l</span>}}_{\mathrm{<span><span>i</span>i</span>}}}<span><span>+</span>+</span>{\mathrm{<span><span>U</span>u</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}^{\mathrm{<span><span>H</span>h</span>}}{\mathrm{<span><span>n</span>no</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}}$

其中，表示基站l到用户g_k的平坦瑞利衰落信道，表示基站g传输给用户g_k的信号，表示用户g_k接收到的噪声，为独立同分布的复高斯向量，满足表示维度为Kd×d的复矩阵，表示维度为N_t×Kd的复矩阵，表示维度为d×N_r的复矩阵；in, Denotes the flat Rayleigh fading channel from base station l to user g_k , Indicates the signal transmitted by base station g to user g_k , Indicates the noise received by user g_k , which is an independent and identically distributed complex Gaussian vector, satisfying Represents a complex matrix of dimension Kd×d, Represents a complex matrix of dimension N_t ×Kd, Represents a complex matrix of dimension d×N_r ;

图3所示为本发明实施流程图，具体包括如下步骤：Fig. 3 shows that the implementation flow chart of the present invention specifically comprises the following steps:

步骤301，设计基站内层预编码矩阵将ICI信号对齐在一个低维子空间内。这样，来自其它小区的干扰信号可以表示为：Step 301, designing the inner layer precoding matrix of the base station Align the ICI signals within a low-dimensional subspace. In this way, interference signals from other cells can be expressed as:

接收端运用迫零技术消除ICI信号，因此，为了接收到d个无干扰的数据流，需要接收端天线数N_r≥(G-1)Kd+d。本方案通过预编码矩阵将来自不同基站的干扰信号对齐在同一低维子空间，对于小区g中的用户k而言，就是将来自其他小区的干扰一一对齐到来自第g+1小区的干扰信号子空间即：$\mathrm{span}\left(G_{g_k,g+1}\right)=\mathrm{span}\left(H_{g_k,1}{P}_1\right)=...=\mathrm{span}\left(H_{g_k,g-1}{P}_{g-1}\right)=\mathrm{span}\left(H_{g_k,g+2}{P}_{g+2}\right)=...=\mathrm{span}\left(H_{g_k,G}{P}_G\right)$，其中，span()表示矩阵的列向量张成的子空间。The receiving end uses zero-forcing technology to eliminate ICI signals. Therefore, in order to receive d interference-free data streams, the number of antennas N_r ≥ (G-1)Kd+d at the receiving end is required. This scheme uses the precoding matrix Aligning the interference signals from different base stations in the same low-dimensional subspace, for user k in cell g, is to align the interference from other cells to the interference signal subspace from the g+1th cell Right now:$\mathrm{span}\left(G_{g_k,g+1}\right)=\mathrm{span}\left(h_{g_k,1}{P}_1\right)=...=\mathrm{span}\left(h_{g_k,g-1}{P}_{g-1}\right)=\mathrm{span}\left(h_{g_k,g+2}{P}_{g+2}\right)=...=\mathrm{span}\left(h_{g_k,G}{P}_G\right)$ , where span() represents the subspace spanned by the column vectors of the matrix.

由于初等列变换不会改变一个矩阵的列空间，通过增强约束条件，上式可写为：Since the elementary column transformation will not change the column space of a matrix, by enhancing the constraints, the above formula can be written as:

${\mathrm{<span><span>G</span>G</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>g</span>g</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>Q</span>Q</span>}}_{\mathrm{<span><span>g</span>g</span>}\mathrm{<span><span>1</span>1</span>}}<span><span>=</span>=</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>=</span>=</span>{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>g</span>g</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>g</span>g</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>Q</span>Q</span>}}_{\mathrm{<span><span>g</span>g</span>}<span><span>(</span>(</span>\mathrm{<span><span>g</span>g</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>}<span><span>=</span>=</span>{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>g</span>g</span>}<span><span>+</span>+</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>g</span>g</span>}<span><span>+</span>+</span>\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>Q</span>Q</span>}}_{\mathrm{<span><span>g</span>g</span>}<span><span>(</span>(</span>\mathrm{<span><span>g</span>g</span>}<span><span>+</span>+</span>\mathrm{<span><span>2</span>2</span>}<span><span>)</span>)</span>}<span><span>=</span>=</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>=</span>=</span>{\mathrm{<span><span>H</span>h</span>}}_{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>,</span>,</span>\mathrm{<span><span>G</span>G</span>}}{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>G</span>G</span>}}{\mathrm{<span><span>Q</span>Q</span>}}_{\mathrm{<span><span>gG</span>gG</span>}}<span><span>,</span>,</span>$

其中，{Q_gl}可为Kd阶非奇异方阵，也可为非零常数。Among them, {Q_gl } can be a non-singular square matrix of order Kd, or a non-zero constant.

根据克罗内克积性质上式进一步可写为：$\left\{\begin{array}{c}(I\&CircleTimes;H_{g_k,g+1})\mathrm{vec}\left(P_{g+1}\right)=(Q_{g1}\&CircleTimes;H_{g_k,1})\mathrm{vec}\left(P_1\right)\\ .\\ .\\ .\\ (I\&CircleTimes;H_{g_k,g+1})\mathrm{vec}\left(P_{g+1}\right)=(Q_{g(g-1)}\&CircleTimes;H_{g_k,g-1})\mathrm{vec}\left(P_{g-1}\right)\\ (I\&CircleTimes;H_{g_k,g+1})\mathrm{vec}\left(P_{g+1}\right)=(Q_{g(g+2)}\&CircleTimes;H_{g_k,g+2})\mathrm{vec}\left(P_{g+2}\right)\\ .\\ .\\ .\\ (I\&CircleTimes;H_{g_k,g+1})\mathrm{vec}\left(P_{g+1}\right)=(Q_{\mathrm{gG}}\&CircleTimes;H_{g_k,G})\mathrm{vec}\left(P_G\right)\end{array}\right.,$其中，I是与{Q_gl}同阶的单位阵；()^T表示求取矩阵的转置，vec()表示求取矩阵的列向量化函数。此时，小区间干扰信号因此可知，通过以上处理可有效地减少用户天线数。According to the Kronecker product property The above formula can be further written as:$\left\{\begin{array}{c}(I\&CircleTimes;h_{g_k,g+1})\mathrm{vec}\left(P_{g+1}\right)=(Q_{g1}\&CircleTimes;h_{g_k,1})\mathrm{vec}\left(P_1\right)\\ .\\ .\\ .\\ (I\&CircleTimes;h_{g_k,g+1})\mathrm{vec}\left(P_{g+1}\right)=(Q_{g(g-1)}\&CircleTimes;h_{g_k,g-1})\mathrm{vec}\left(P_{g-1}\right)\\ (I\&CircleTimes;h_{g_k,g+1})\mathrm{vec}\left(P_{g+1}\right)=(Q_{g(g+2)}\&CircleTimes;h_{g_k,g+2})\mathrm{vec}\left(P_{g+2}\right)\\ .\\ .\\ .\\ (I\&CircleTimes;h_{g_k,g+1})\mathrm{vec}\left(P_{g+1}\right)=(Q_{\mathrm{gG}}\&CircleTimes;h_{g_k,G})\mathrm{vec}\left(P_G\right)\end{array}\right.,$ Among them, I is the identity matrix with the same order as {Q_gl }; ()^T means to obtain the transpose of the matrix, and vec() represents the column vectorization function to obtain the matrix. At this time, inter-cell interference signals Therefore, it can be seen that the number of user antennas can be effectively reduced through the above processing.

对于整个系统而言，小区间的干扰信号都被对齐在来自下一个小区的干扰子空间内，基站外层预编码矩阵需满足下式：For the entire system, the interference signals between cells are aligned in the interference subspace from the next cell, and the outer precoding matrix of the base station The following formula needs to be satisfied:

$\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>H</span>h</span>}}\mathrm{<span><span>p</span>p</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}$

$\mathrm{<span><span>p</span>p</span>}<span><span>=</span>=</span>\left[\begin{array}{c}\mathrm{<span><span>vec</span>vec</span>}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>)</span>)</span>\\ \mathrm{<span><span>vec</span>vec</span>}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ <span><span>.</span>.</span>\\ \mathrm{<span><span>vec</span>vec</span>}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>G</span>G</span>}}<span><span>)</span>)</span>\end{array}\right]$

其中，I是与{Q_gl}(g≠l；g,l＝1,...G)同阶的单位阵；Wherein, I is an identity matrix with the same order as {Q_gl }(g≠l; g,l=1,...G);

表示基站l到小区g的平坦瑞利衰落信道，表示基站g外层预编码矩阵，P₁表示基站1的外层预编码矩阵，即P₂表示基站2的外层预编码矩阵，O表示KdKN_r×KdN_t维的零矩阵；矩阵 Denotes the flat Rayleigh fading channel from base station l to cell g, Represents the outer precoding matrix of base station g, P₁ represents the outer precoding matrix of base station 1, that is, P₂ represents the outer precoding matrix of base station 2, O represents the zero matrix of KdKN_r ×KdN_t dimension; matrix

矩阵中每个矩阵块(如：O,)都是维度相同的矩阵，若将每个矩阵块都看成一个元素，那么矩阵有(G-2)G行、G列，每一行都只有2个元素不是O，第一个(G-2)行是为了将小区1中用户接收到的ICI信号对齐，第二个(G-2)行是为了将小区2中用户接收到的ICI信号对齐，以此类推。matrix Each matrix block in (eg: O, ) are all matrices with the same dimension. If each matrix block is regarded as an element, then the matrix There are (G-2) G rows and G columns, and each row has only 2 elements that are not O. The first (G-2) row is to align the ICI signals received by users in cell 1, and the second (G Line -2) is for aligning the ICI signals received by users in cell 2, and so on.

为了具体且简单地阐述外层预编码矩阵的设计思想，下面将G＝3以为例进行分析，对齐小区间干扰信号需满足In order to specifically and briefly illustrate the outer precoding matrix The design idea of G=3 will be analyzed below as an example, and the alignment of interference signals between cells needs to satisfy

下式：The following formula:

$\left[\begin{array}{ccc}\mathrm{<span><span>O</span>o</span>}& \mathrm{<span><span>I</span>I</span>}<span><span>\&CircleTimes;</span>\&CircleTimes;</span>{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>12</span>12</span>}}& <span><span>-</span>-</span>{\mathrm{<span><span>Q</span>Q</span>}}_{\mathrm{<span><span>13</span>13</span>}}^{\mathrm{<span><span>T</span>T</span>}}<span><span>\&CircleTimes;</span>\&CircleTimes;</span>{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>13</span>13</span>}}\\ <span><span>-</span>-</span>{\mathrm{<span><span>Q</span>Q</span>}}_{\mathrm{<span><span>21</span>twenty\; one</span>}}^{\mathrm{<span><span>T</span>T</span>}}<span><span>\&CircleTimes;</span>\&CircleTimes;</span>{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>21</span>twenty\; one</span>}}& \mathrm{<span><span>O</span>o</span>}& \mathrm{<span><span>I</span>I</span>}<span><span>\&CircleTimes;</span>\&CircleTimes;</span>{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>23</span>twenty\; three</span>}}\\ \mathrm{<span><span>I</span>I</span>}<span><span>\&CircleTimes;</span>\&CircleTimes;</span>{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>31</span>31</span>}}& <span><span>-</span>-</span>{\mathrm{<span><span>Q</span>Q</span>}}_{\mathrm{<span><span>32</span>32</span>}}^{\mathrm{<span><span>T</span>T</span>}}<span><span>\&CircleTimes;</span>\&CircleTimes;</span>{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>32</span>32</span>}}& \mathrm{<span><span>O</span>o</span>}\end{array}\right]\left[\begin{array}{c}\mathrm{<span><span>vec</span>vec</span>}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>)</span>)</span>\\ \mathrm{<span><span>vec</span>vec</span>}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>\\ \mathrm{<span><span>vec</span>vec</span>}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>3</span>3</span>}}<span><span>)</span>)</span>\end{array}\right]<span><span>=</span>=</span>\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>H</span>h</span>}}\mathrm{<span><span>p</span>p</span>}<span><span>=</span>=</span>\mathrm{<span><span>0</span>0</span>}$

其中，$p=\left[\begin{array}{c}\mathrm{vec}\left(P_1\right)\\ \mathrm{vec}\left(P_2\right)\\ \mathrm{vec}\left(P_3\right)\end{array}\right]=\left[\begin{array}{c}{p}_1\\ p_2\\ p_3\end{array}\right].$in,$p=\left[\begin{array}{c}\mathrm{vec}\left(P_1\right)\\ \mathrm{vec}\left(P_2\right)\\ \mathrm{vec}\left(P_3\right)\end{array}\right]=\left[\begin{array}{c}{p}_1\\ p_2\\ p_3\end{array}\right].$

3011：在N_t＞KN_r时，{Q_gl}(g≠l；g,l＝1,...G)可为任意Kd阶非奇异矩阵，也可为任意非零常数，p都有非零解。3011: When N_t >KN_r , {Q_gl }(g≠l; g,l=1,...G) can be any non-singular matrix of Kd order, or any non-zero constant, p has non-zero solution.

3012：在N_t≤KN_r时，上式要有非零解，矩阵{Q_gl}(g≠l；g,l＝1,...G)需要满足，使或者使接近于0，最终求解出p。此时，秩限制问题就可以转变为下述的最优化问题：在已知{Q_gl}(g≠l；g,l＝1,...G)的情况下，方程的最优解p是矩阵的最小特征值对应的特征向量。此外，$\underset{p,\left\{Q_{\mathrm{gl}}\right\}}{\min }{\left|\right|\tilde{H}p\left|\right|}^2=\underset{p,\left\{Q_{\mathrm{gl}}\right\}}{\min }({\left|\right|I\&CircleTimes;H_{12}{p}_2-Q_{13}^T\&CircleTimes;H_{13}{p}_3\left|\right|}^2+{\left|\right|I\&CircleTimes;H_{23}{p}_3-Q_{21}^T\&CircleTimes;H_{21}{p}_1\left|\right|}^2+{\left|\right|I\&CircleTimes;H_{31}{p}_1-Q_{32}^T\&CircleTimes;H_{32}{p}_2\left|\right|}^2)$，根据最小二乘解，可知Q₁₃＝((H₁₃p₃)^HH₁₃p₃)^-1(H₁₃p₃)^H(H₁₂p₂)，Q₂₁,Q₃₂的求解也类似于Q₁₃。接着，通过循环迭代向量p和矩阵{Q_gl}(g≠l；g,l＝1,...G)，得到最优解。其中，rank()表示求取矩阵的秩，||||表示求取向量的2-范数。3012: When N_t ≤ KN_r , the above formula must have a non-zero solution, and the matrix {Q_gl }(g≠l; g,l=1,...G) needs to be satisfied, so that or make is close to 0, and p is finally solved. At this point, the rank-limited problem can be transformed into the following optimization problem: In the case of known {Q_gl }(g≠l; g,l=1,...G), the optimal solution p of the equation is the matrix The eigenvector corresponding to the smallest eigenvalue of . also,$\underset{p,\left\{Q_{\mathrm{gl}}\right\}}{\min }{\left|\right|\tilde{h}p\left|\right|}^2=\underset{p,\left\{Q_{\mathrm{gl}}\right\}}{\min }({\left|\right|I\&CircleTimes;h_{12}{p}_2-Q_{13}^T\&CircleTimes;h_{13}{p}_3\left|\right|}^2+{\left|\right|I\&CircleTimes;h_{\mathrm{twenty\; three}}{p}_3-Q_{\mathrm{twenty\; one}}^T\&CircleTimes;h_{\mathrm{twenty\; one}}{p}_1\left|\right|}^2+{\left|\right|I\&CircleTimes;h_{31}{p}_1-Q_{32}^T\&CircleTimes;h_{32}{p}_2\left|\right|}^2)$ , according to the least squares solution, it can be known that Q₁₃ =((H₁₃ p₃ )^H H₁₃ p₃ )^-1 (H₁₃ p₃ )^H (H₁₂ p₂ ), the solutions of Q₂₁ and Q₃₂ are also similar to Q₁₃ . Next, the optimal solution is obtained by cyclically iterating the vector p and the matrix {Q_gl } (g≠l; g, l=1, . . . G). Among them, rank() means to find the rank of the matrix, and |||| means to find the 2-norm of the vector.

将此循环算法的步骤概述如下：1)初始化任意Kd阶非奇异方阵{Q_gl}(g≠l；g,l＝1,...G)；2)求解矩阵的最小特征值对应的特征向量p；3)根据最小二乘解求解{Q_gl}(g≠l；g,l＝1,...G)；4)重复2)、3)步骤，直至ε是一个非负数。The steps of this cyclic algorithm are summarized as follows: 1) Initialize any Kd-order non-singular square matrix {Q_gl }(g≠l; g,l=1,...G); 2) Solve the matrix eigenvector p corresponding to the minimum eigenvalue of ; 3) Solve {Q_gl }(g≠l; g,l=1,...G) according to the least squares solution; 4) Repeat steps 2) and 3) until ε is a non-negative number.

3013：当N_t＝KN_r时，{Q_gl}(g≠l；g,l＝1,...G)只需为非零常数，为方便区分，将非零常数{Q_gl}(g≠l；g,l＝1,...G)记为{a_gl}(g≠l；g,l＝1,...G)，通过闭式求解得到预编码矩阵此时，矩阵等价于$\det \left\{\tilde{H}\right\}=0.$通过矩阵运算，可以得到：其中，$b={(-1)}^{N_t}\det \left(H_{23}{H}_{32}{H}_{13}{H}_{23}^{-1}{H}_{21}\right)$和$\mathrm{\&Omega;}=-H_{21}^{-1}{H}_{23}{H}_{13}^{-1}{H}_{12}{H}_{32}^{-1}{H}_{31}.$当-a₃₂a₁₃a₂₁等于Ω的特征值时，成立。其中，det{}表示求取矩阵的行列式值。3013: When N_t ＝KN_r , {Q_gl }(g≠l; g,l=1,...G) only needs to be a non-zero constant. For the convenience of distinction, the non-zero constant {Q_gl }( g≠l; g, l=1,...G) is recorded as {a_gl }(g≠l; g, l=1,...G), and the precoding matrix is obtained by closed-form solution At this point, the matrix Equivalent to$\det \left\{\tilde{h}\right\}=0.$ Through matrix operations, we can get: in,$b={(-1)}^{N_t}\det \left(h_{\mathrm{twenty\; three}}{h}_{32}{h}_{13}{h}_{\mathrm{twenty\; three}}^{-1}{h}_{\mathrm{twenty\; one}}\right)$ and$\mathrm{\&Omega;}=-h_{\mathrm{twenty\; one}}^{-1}{h}_{\mathrm{twenty\; three}}{h}_{13}^{-1}{h}_{12}{h}_{32}^{-1}{h}_{31}.$ When -a₃₂ a₁₃ a₂₁ is equal to the eigenvalue of Ω, established. Among them, det{} means to find the determinant value of the matrix.

步骤302，设计接收矩阵以消除ICI信号，因此，是ICI信号的零空间，其中，G为小区数，K为小区内用户数，N_r为用户配置的天线数，每个用户对应d个数据流，表示维度为d×N_r的复矩阵，()^H表示求取矩阵的共轭转置。Step 302, design receiving matrix to cancel the ICI signal, therefore, is the null space of the ICI signal, where G is the number of cells, K is the number of users in the cell, N_r is the number of antennas configured by users, and each user corresponds to d data streams, Represents a complex matrix with a dimension of d×N_r , and ()^H represents the conjugate transpose of the matrix.

步骤303，设计基站内层预编码矩阵以消除IUI信号，因此，是IUI信号的零空间。即：Step 303, designing the inner layer precoding matrix of the base station to eliminate the IUI signal, therefore, is the null space of the IUI signal. Right now:

$B_{g_k}\&Subset;\mathrm{null}\left({[{\left(U_{g_1}^H{H}_{g_1,g}{P}_g\right)}^H,...,{\left(U_{g_{k-1}}^H{H}_{g_{k-1},g}{P}_g\right)}^H,{\left(U_{g_{k+1}}^H{H}_{g_{k+1},g}{P}_g\right)}^H,...,{\left(U_{g_k}^H{H}_{g_k,g}{P}_g\right)}^H]}^H\right)$。其中，表示接收矩阵，表示基站到本小区用户的平坦瑞利衰落信道，P_g表示基站g的外层预编码矩阵。G为小区数，K为小区内用户数，每个用户对应d个自由度，表示维度为Kd×d的复矩阵，表示维度为d×N_r的复矩阵，()^H表示求取矩阵的共轭转置，null()表示求取矩阵的零空间。$B_{g_k}\&Subset;\mathrm{null}\left({[{\left(u_{g_1}^h{h}_{g_1,g}{P}_g\right)}^h,...,{\left(u_{g_{k-1}}^h{h}_{g_{k-1},g}{P}_g\right)}^h,{\left(u_{g_{k+1}}^h{h}_{g_{k+1},g}{P}_g\right)}^h,...,{\left(u_{g_k}^h{h}_{g_k,g}{P}_g\right)}^h]}^h\right)$ . in, represents the receiving matrix, Indicates the flat Rayleigh fading channel from the base station to the users in the cell, and P_g indicates the outer precoding matrix of the base station g. G is the number of cells, K is the number of users in the cell, each user corresponds to d degrees of freedom, Represents a complex matrix of dimension Kd×d, Represents a complex matrix with a dimension of d×N_r , ()^H represents the conjugate transpose of the matrix, and null() represents the null space of the matrix.

至此，IUI信号被对齐在的正交子空间内，ICI信号也被对齐或逼近到的正交子空间内，多小区MIMO-IFBC系统的干扰信号得以消除，如图4所示。其中，span()表示矩阵的列向量张成的子空间。图4中符号表示见上文。At this point, the IUI signal is aligned at In the orthogonal subspace of , the ICI signal is also aligned or approximated to In the orthogonal subspace of , the interference signal of the multi-cell MIMO-IFBC system is eliminated, as shown in Figure 4. Among them, span() represents the subspace spanned by the column vectors of the matrix. See above for symbol representation in Figure 4.

另外，我们也可以将来自第g+1小区的干扰信号对齐在来自于剩余小区干扰信号组成的子空间内，即将来自第g+1小区的干扰信号表示为来自剩余小区干扰信号的线性组合，这时预编码矩阵{P_g}满足下式：In addition, we can also align the interference signal from the g+1th cell in the subspace composed of the interference signals from the remaining cells, that is, express the interference signal from the g+1th cell as a linear combination of the interference signals from the remaining cells, At this time, the precoding matrix {P_g } satisfies the following formula:

此时，来自相邻小区的ICI信号表示为：At this time, the ICI signal from the neighboring cell is expressed as:

此方案所需接收端天线数比上述方案的接收端天线数有所增加，但所需基站天线数却减少。因此，在不同场景下，可以选择不同ICI信号对齐方案。The number of receiving end antennas required by this solution is increased compared with the above solution, but the number of required base station antennas is reduced. Therefore, in different scenarios, different ICI signal alignment schemes can be selected.

图5所示为(4,13)×(2,3)、(4,12)×(2,3)、(4,11)×(2,3)系统配置下，基站给每个用户发送的数据流个数d＝1，总自由度DoF＝8时的系统容量仿真图。当基站天线数N_t≥13，即满足N_t＞(G-2)KNr时，ICI信号能被完全对齐在同一低维子空间内，即的正交子空间；当基站天线数N_t≤(G-2)KN_r时，通过设计非奇异阵Q，也能将小区间干扰信号对齐或逼近到的正交子空间内。由图5的结果可以看出，在基站天线数N_t＝12,11，略小于临界值13时，ICI信号也几乎能被完全消除，系统容量的微少下降，主要是由基站天线数减少引起的。本发明通过在基站设置双层预编码，有效地减少了用户天线数和处理复杂度，节约了移动设备设计成本，同时能够有效地消除多小区MIMO-IBC系统中的ICI信号和IUI信号。Figure 5 shows (4,13)×(2,3), (4,12)×(2,3), (4,11)×(2,3) system configurations, the base station sends The simulation diagram of the system capacity when the number of data streams d=1 and the total degree of freedom DoF=8. When the number of base station antennas N_t ≥ 13, that is, when N_t > (G-2)KNr, the ICI signals can be completely aligned in the same low-dimensional subspace, namely The orthogonal subspace of ; when the number of base station antennas N_t ≤ (G-2)KN_r , by designing a non-singular array Q, the inter-cell interference signals can also be aligned or approximated to in the orthogonal subspace of . From the results in Figure 5, it can be seen that when the number of base station antennas N_t = 12,11, which is slightly less than the critical value of 13, the ICI signal can be almost completely eliminated, and the slight decrease in system capacity is mainly caused by the reduction in the number of base station antennas of. The invention effectively reduces the number of user antennas and processing complexity by setting double-layer precoding in the base station, saves the design cost of mobile equipment, and can effectively eliminate ICI signals and IUI signals in a multi-cell MIMO-IBC system.

Claims (7)

1. The interference alignment method based on the two-layer precoding structure in the multi-input multi-output interference broadcast channel system is characterized by comprising the following steps: constructing any Kd order nonsingular matrix (Q)_glDesigning an outer precoding matrix of the base stationAligning all ICI signals in a low-dimensional interference subspace; receiving end design receiving matrixTo cancel the ICI signal; designing inner pre-coding matrix of base stationTo cancel IUI signals, wherein l 1.. G, G1.. G; k1, K, G being the number of cells in the system, K being the number of users in each cell, N_tAnd N_rThe number of antennas configured for the base station and the user, d is the data stream corresponding to each user,with a representation dimension of N_tA complex matrix of x Kd,with a representation dimension of dXN_rThe complex matrix of (a) is then formed,complex matrix of dimension Kd × d, ()^HIndicating the conjugate transpose of the matrix being solved for.

2. The method according to claim 1, wherein aligning all ICI signals in a low-dimensional interference subspace comprises: for users in a cell g, aligning or approximating ICI signals to an interference signal subspace from a g +1 cell, and a base station outer layer precoding matrix P_gSatisfies the formula:

$\tilde{H}p=0$

$p=\left[\begin{array}{c}\mathrm{vec}\left(P_1\right)\\ \mathrm{vec}\left(P_2\right)\\ .\\ .\\ .\\ \mathrm{vec}\left(P_G\right)\end{array}\right]$

wherein Q is_glIs Kd order nonsingular matrix, I is AND Q_glUnit array of the same order, H_glRepresenting a flat Rayleigh fading channel, P, from base station l to cell g_gAn outer layer precoding matrix of a base station g is represented, and g is not equal to l; g, l ═ 1.. G, O denotes KdkN_r×KdN_tZero matrix, matrix of dimensionsThe expression dimension is (G-2) GKKDKN_r×GKdN_tComplex matrix of (c) ()^TRepresenting the transpose of the solved matrix, vec () representing the column vectorization function of the solved matrix.

3. The method of claim 1Method, characterized in that the interfering signals from g +1 cells are aligned into the subspace formed by the interfering signals from the remaining cells, the outer precoding matrix P of the base station_gSatisfies the formula:

wherein Q is_glIs Kd order nonsingular matrix, I is AND Q_glUnit array of the same order, H_glRepresenting a flat Rayleigh fading channel, P, from base station l to cell g_gDenotes the outer precoding matrix of the base station g, O denotes KdkN_r×KdN_tZero matrix, matrix of dimensionsThe expression dimension is GKdKN_r×GKdN_tComplex matrix of (c) ()^TRepresenting the transpose of the solved matrix, vec () representing the column vectorization function of the solved matrix.

4. A method according to one of claims 1-3, characterized in that the receiving matrix is a matrixIs the null space of the ICI signal, where,with a representation dimension of dXN_rThe complex matrix of (a).

5. Method according to one of claims 1 to 3, characterized in that the inner precoding matrix B of the base station is designed_gkIs the null space of the IUI signal, where,a complex matrix with dimensions Kd × d is represented.

6. A method according to one of claims 1 to 3, characterized in that the receiving matrix at the receiving end divides the signal space into an interference signal subspace to which inter-user interference signals and inter-cell interference signals are aligned and a desired signal subspace to which desired signals are aligned, the dimensions of the desired signal subspace being greater than or equal to the number of data streams to be transmitted.

7. The method of claim 2, wherein when N is_t＞(G-2)KN_rTime, matrix Q_glIs any Kd order nonsingular matrix or any nonzero constant; when N is present_t＜(G-2)KN_rWhile iterating the matrix Q through the loop_glAnd a vector p, such thatOr makeIs close to 0; when N is present_t＝(G-2)KN_rTime, matrix Q_glIs a non-zero constant. Wherein,is a dimension of (G-2) GKdkK_r×GKdN_tThe elements of the complex matrix are composed of a channel matrix and a non-singular matrix Q_glFormed by the elements of the vector P being the outer precoding matrix P of the base station_gThe rank () represents the rank of the solution matrix, and | | represents the 2-norm of the solution vector.